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Diffusion creep refers to the
deformation Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * Defo ...
of
crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...
solids by the
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
of vacancies through their
crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_ ...
. Diffusion creep results in
plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strai ...
rather than brittle failure of the material. Diffusion creep is more sensitive to
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
than other
deformation mechanism A deformation mechanism, in geology, is a process occurring at a microscopic scale that is responsible for changes in a material's internal structure, shape and volume. The process involves planar discontinuity and/or displacement of atoms from th ...
s. It usually takes place at high
homologous temperature Homologous temperature expresses the thermodynamic temperature of a material as a fraction of the thermodynamic temperature of its melting point (i.e. using the Kelvin scale): T_H = \frac For example, the homologous temperature of lead at room ...
s (i.e. within about a tenth of its absolute
melting Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which incre ...
temperature). Diffusion creep is caused by the migration of crystalline defects through the lattice of a crystal such that when a crystal is subjected to a greater degree of compression in one direction relative to another, defects migrate to the crystal faces along the direction of compression, causing a net mass transfer that shortens the crystal in the direction of maximum compression. The migration of defects is in part due to vacancies, whose migration is equal to a net mass transport in the opposite direction.


Principle

Crystalline materials are never perfect on a microscale. Some sites of atoms in the crystal lattice can be occupied by point defects, such as "alien" particles or vacancies. Vacancies can actually be thought of as chemical species themselves (or part of a compound species/component) that may then be treated using heterogeneous phase equilibria. The number of vacancies may also be influenced by the number of chemical impurities in the crystal lattice, if such impurities require the formation of vacancies to exist in the lattice. A vacancy can move through the crystal structure when the neighbouring particle "jumps" in the vacancy, so that the vacancy moves in effect one site in the crystal lattice.
Chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing o ...
s need to be broken and new bonds have to be formed during the process, therefore a certain
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
is needed. Moving a vacancy through a crystal becomes therefore easier when the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
is higher. The most stable state will be when all vacancies are evenly spread through the crystal. This principle follows from
Fick's law Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion e ...
: : J_x = -D_x \frac In which ''Jx'' stands for the
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport p ...
("flow") of vacancies in direction ''x''; ''D''''x'' is a constant for the material in that direction and / is the difference in concentration of vacancies in that direction. The law is valid for all principal directions in (''x'', ''y'', ''z'')-space, so the ''x'' in the formula can be exchanged for ''y'' or ''z''. The result will be that they will become evenly distributed over the crystal, which will result in the highest mixing entropy. When a
mechanical stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...
is applied to the crystal, new vacancies will be created at the sides perpendicular to the direction of the lowest
principal stress In continuum mechanics, the Cauchy stress tensor \boldsymbol\sigma, true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components \sigma_ that completely ...
. The vacancies will start moving in the direction of crystal planes perpendicular to the maximal stress. Current theory holds that the
elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togethe ...
strain in the neighborhood of a defect is smaller toward the axis of greatest differential compression, creating a defect chemical
potential gradient In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because ...
(depending upon lattice strain) within the crystal that leads to net accumulation of defects at the faces of maximum compression by diffusion. A flow of vacancies is the same as a flow of particles in the opposite direction. This means a crystalline material can deform under a differential stress, by the flow of vacancies. Highly mobile chemical components substituting for other species in the lattice can also cause a net differential mass transfer (i.e. segregation) of chemical species inside the crystal itself, often promoting shortening of the rheologically more difficult substance and enhancing deformation.


Types of diffusion creep

Diffusion of vacancies through a crystal can happen in a number of ways. When vacancies move through the crystal (in the material sciences often called a "grain"), this is called '' Nabarro–Herring creep''. Another way in which vacancies can move is along the
grain boundaries In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal ...
, a mechanism called '' Coble creep''. When a crystal deforms by diffusion creep to accommodate space problems from simultaneous grain boundary sliding (the movement of whole grains along grain boundaries) this is called '' granular or superplastic flow''. Diffusion creep can also be simultaneous with
pressure solution In structural geology and diagenesis, pressure solution or pressure dissolution is a deformation mechanism that involves the dissolution of minerals at grain-to-grain contacts into an aqueous pore fluid in areas of relatively high stress and ...
. Pressure solution is, like Coble creep, a mechanism in which material moves along grain boundaries. While in Coble creep the particles move by "dry" diffusion, in pressure solution they move in solution.


Flow laws

Each plastic deformation of a material can be described by a formula in which the
strain rate In materials science, strain rate is the change in strain (deformation) of a material with respect to time. The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change w ...
(\dot) depends on the differential stress (''σ'' or ''σ''D), the grain size (''d'') and an activation value in the form of an
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1 ...
: \!\dot = Ae^\frac \frac In which ''A'' is the constant of diffusion, ''Q'' the activation energy of the mechanism, ''R'' the
gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
and ''T'' the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wo ...
(in
kelvins The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ph ...
). The exponents ''n'' and ''m'' are values for the sensitivity of the flow to stress and grain size respectively. The values of ''A'', ''Q'', ''n'' and ''m'' are different for each deformation mechanism. For diffusion creep, the value of ''n'' is usually around 1. The value for ''m'' can vary between 2 (Nabarro-Herring creep) and 3 (Coble creep). That means Coble creep is more sensitive to grain size of a material: materials with larger grains can deform less easily by Coble creep than materials with small grains.


Traces of diffusion creep

It is difficult to find clear microscale evidence for diffusion creep in a crystalline material, since few structures have been identified as definite proof. A material that was deformed by diffusion creep can have flattened grains (grains with a so called shape-preferred orientation or SPO). Equidimensional grains with no lattice-preferred orientation (or LPO) can be an indication for superplastic flow. In materials that were deformed under very high temperatures, lobate grain boundaries may be taken as evidence for diffusion creep.Gower & Simpson 1992 Diffusion creep is a mechanism by which the volume of the crystals can increase. Larger grain sizes can be a sign that diffusion creep was more effective in a crystalline material.


See also

*
Creep (deformation) In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as a result of long-term exposure to high lev ...
*
Deformation (engineering) In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
*
Diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
* Dislocation creep * Material sciences


References


Literature

*Gower, R.J.W. & Simpson, C.; 1992: ''Phase boundary mobility in naturally deformed, high-grade quartzofeldspatic rocks: evidence for diffusion creep'', Journal of Structural Geology 14, p. 301-314. *Passchier, C.W. & Trouw, R.A.J., 1998: ''Microtectonics'', Springer, *Twiss, R.J. & Moores, E.M., 2000 (6th edition): ''Structural Geology'', W.H. Freeman & co, {{ISBN, 0-7167-2252-6 Materials degradation